Successfully complete the indicated task to unlock the corresponding item for purchase at the store:

Bionic Beanie: Successfully complete "Lunacy".

WCC Flag: Successfully complete "High Five".

Singing turrets

There is a turret inside a ventilation grate just past the elevator in Test Chamber 16. Jump over it, get the Refraction Cube, then use the laser to destroy that turret to open the grate. Enter the new area to find four turrets singing a song.

Easy "Door Prize" trophy

In Chapter 6: The Fall, there are six sealed metal doors marked "VITRIFIED" (Vitrified Doors) that have buttons in front of them that play unique audio clips of Cave speaking. At the beginning of Chapter 6, you will have to penetrate the 1960s Aperture facility. After flying through the Aperture logo, you will come to an area with a tall elevator. You must use the elevator shaft as a gravity boost to get across a chasm. On one end of the chasm is a platform with three of the Vitrified Doors. Listen to the audio that plays when you hit the buttons in front of each of the sealed doors. Then, play through the level until you reach the 1971-era test facility. When Cave starts talking about testing on hobos, below one of the test spheres and a giant Aperture logo is a room marked "CONTROL ROOM" in yellow lettering. You can use a portal to get high above the Control Room and enter a small office. In the corner of this office is a cabinet with a door behind it. Enter this door to find a secret hallway that leads to a dock (where you get the "Ship Overboard" trophy). The final three Vitrified Doors can be found in this area.

Easy "Final Transmission" trophy

In Chapter 2, Test Chamber 6, carry a radio (which shows up in a clump of garbage after you hit a button) into a window above the chamber. Once you get the radio, backtrack through the level, and place a portal on the pad across from the window. Use the launchers to get through the portal and into the room beyond the window with radio in hand. Once there, carry the radio up to the wall to get the "Final Transmission" trophy.

Easy "No Hard Feelings" trophy

Play through Chapter 5: The Escape until you reach the conveyor belts carrying droids to the incinerator. Use a portal to get onto the conveyor belt, then walk on it until a droid with a working laser beam appears. Pick it up to get the "No Hard Feelings" trophy.

Easy "Overclocker" trophy

Easy "Pit Boss" trophy

At the beginning of Chapter 9, after Wheatley's Surprise, you will need to use a portal to get away from the platform just as Wheatley sends a bunch of arms to crush you. Instead of continuing to run away on the catwalks, stay nearby. Wheatly will plead with you to come back. Stand at the edge of the pit overlooking his trap, and he will ask you to jump in the pit. Do so to get the "Pit Boss" trophy.

Easy "Portrait Of A Lady" trophy

At the beginning of Chapter 7: The Reunion, while facing the entrance to the 02 room on the catwalks between tests 1971-01 and 1971-02, place a portal on the wall to your right, and look for another pad you can shoot a portal onto through the gate and past the stairs to the left. On the other side of the portal is an office with a large portrait of Cave Johnson and Caroline. Stare at the portrait, and GLadOS will comment on it, and you will get the "Portrait Of A Lady" trophy.

At the end of Chapter 2, Test Chamber 7, shoot a blue portal on the other side of the entrance to the exit of the area. Then, grab the Companion Cube that is depressing the button, and use an orange portal to get the Companion Cube to the exit without it getting disintegrated and get the "Preservation Of Mass" trophy.

Easy "Schrodinger's Catch" trophy

Play through Chapter 6: The Fall until you reach the 1958-28 room. In this room is a cube trapped in a glass box, with Blue Gel streaming out of a pipe in a corner. Save the game when entering this room so you can retry the puzzle if you fail. You must shoot a portal under the gel and over the crate to coat the cube in goo. The cube will then bounce around until it breaks the glass. Eventually it will break out of the glass. You must catch the cube before it touches the ground to get the "Schrodinger's Catch" trophy. Stand between the entrance and the gel spout to hopefully catch the cube when it comes flying out.

Easy "Ship Overboard" trophy

Play through Chapter 6: The Fall until you reach the 1971-era test facility. When Cave starts talking about testing on hobos, below one of the test spheres and a giant Aperture logo is a room marked "CONTROL ROOM" in yellow lettering. You can use a portal to get high above the Control Room and enter a small office. In the corner of this office is a cabinet with a door behind it. Enter this door to find a secret hallway that leads to a dock. At the end of the walkway by the docks, you will find an orange life preserver marked "BOREALIS". Examine this to get the "Ship Overboard" trophy. This is a reference to the Aperture ship Borealis seen at the end of Half-Life 2: Episode 2.